Renormalised singular stochastic PDEs

Ismael Bailleul, Yvain Bruned

Research output: Working paper

Abstract

Extended decorations on naturally decorated trees were introduced in the work of Bruned, Hairer and Zambotti on algebraic renormalization of regularity structures to provide a convenient framework for the renormalization of systems of singular stochastic PDEs within that setting. This non-dynamical feature of the trees complicated the analysis of the dynamical counterpart of the renormalization process. We provide a new proof of the renormalized system by-passing the use of extended decorations and working for a large class of renormalization maps, with the BPHZ renormalization as a special case. The proof reveals important algebraic properties connected to preparation maps.
Original languageEnglish
PublisherArXiv
Number of pages16
Publication statusPublished - 28 Jan 2021

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